<p>We construct exact solutions that describe the near horizon region of extremal rotating black holes in Einstein-Born-Infeld theory. Using generalized Komar integrals, we extract the electric charge and angular momentum from the near horizon geometries and study their deviations from the Kerr-Newman solution. We identify two features that are direct consequences of the nonlinearities of Born-Infeld theory. First, we find solutions which have vanishing charge but nontrivial electric and magnetic fields. Second, we find that extremal rotating black holes do not exist for sufficiently small charge and angular momentum. Based on analogy with the static black holes, we argue that it would be particularly interesting to construct the full rotating solutions in these parameter regions as they may provide examples of rotating black holes without Cauchy horizons.</p>